Kinematics of the Eye. 693 



Denoting the mean value by Ids 2 , we have 



I= M]> iW + M% + ™ e ) 2 } ddd *- v 



We take the field to be circular, of angular radius a, so 

 that the limits of 6 are and a. The limits of ^ may be 

 taken as and 27r, but it is to be noticed that if <£ be 

 supposed to vary continuously its values at these limits will 

 not be the same. Thus for a given infinitely small value of 

 (j> will be small for o/r = 0; it will change to — it (nearly) as 

 ^ increases from to tt; and again from — it to —2ir 

 (nearly) as sjr further increases from it to 27r. The two sides 

 of the line i|r = are therefore to be included as part of the 

 boundary of the region considered. 



Taking the variation of the integral in the usual manner,, 

 we find 



81= PTsm^^Y"^ 



Jo L OC7 _|0 = O 



Hence we must have 



«*'U™°%hw- ' • • • (7) 



with the boundary conditions 



/||\ ^ =0 for all values of f, . . . (8) 



I g^ + co> 6\ = for all values of 0, . (9) 



the values of S</> for ^ = and -\\r = 2ir being necessarily 

 equal. 



An obvious solution of (7) is 



* = A^ + B, (10) 



which also satisfies the boundary conditions. On reference 

 to (3) we see that in order that the rotation mav vanish 

 for 0->O, in accordance; with our assumption, we must have 



i— w 



and 



